I noticed yesterday my 06 RAM.
20 degrees cold going 25 miph try to
engage 4WD. Light just flashes for 3 mi
when I came to stop for turn went solid.
30 mph tried to diss-engage again went 10 miles before stop
when it went out.
After warming up it seems like I get shorter
blinking. Seems like it
works best when warm and when stopped.
Any thoughts?

 

I always do the change with the truck stopped and in neutral, as indicated on the user manual. It takes only a few seconds.
I know it can be done while running slow, but I believe should be very slow.

 

I believe you are talking about shifting in to 4 low. You can shift into 4 hi either stopped or in motion, including highway speed. It also helps if you release the accelerator momentarily.
Shifting into 4 low you have to be rolling at no more than 2-3mph, or preferably stopped and in neutral.
OP's problem sounds like a weak solenoid or a dodgy connection. My transfer case has consistently shifted between 2 hi and 4 hi in about 5-7 seconds. 2006 Mega Cab